I want to proof the supremum and infimum of the set $A$ is. I can intuitively see that it is $sup(A)=1$ and $inf(A)=0$.
I know I need to proof that 1 is in the upper bound and 0 is in the lower bound, and then that it is the smallest upper and largest lower bound.
The upper bound of $A$ is $1$, as $1/n$ tends to 0 when $n$ gets larger. And the lower bound is $0$ for the same reason.
But how do I reason/proof that they are the smallest upper and largest lower bound?